**EFFECTIVENESS OF A MASTERY LEARNING
INSTRUCTIONAL STRATEGY IN ATTAINMENT OF COMPETENCIES IN MATHEMATICS**

**Shailaja**** P. Shanbhag**

**INTRODUCTION**

**INTRODUCTION**

Teaching of Mathematics,
like that of the other subjects taught at the primary school stage, is
predominantly textbook based, rather than competency based. Especially for
teaching of Mathematics, the conventional approaches seem to be inadequate in
terms of the nature of learning experiences provided and their sequencing.
There seems to be hardly any theoretical basis to follow a particular approach
to teaching of Mathematics. Hence, if
learning experiences are based on some sound psychological principles of
learning and if they take into account the learner characteristics, it must be
possible by a majority of children to attain all the competencies that they are
required to attain in a particular class. Mathematics as a subject has often
been said to be too abstract for some children.
“Any idea, problem, concept or a body of* *knowledge can be presented
in a form that is simple enough for any particular learner to understand it”(Bruner 1966). Hence, the mode of representation of content
is to be planned in such a way that the learner is able to master the
corresponding competency. Presentation of learning experiences from concrete to
semi-abstract to abstract levels may ensure attainment of a competency by every
child.

Mastery learning is an
appropriate strategy to overcome the limitations of the existing system of
instruction at the primary level (Bloom 1968; Block 1971; Guskey
and Gates 1986; and Patterson 1993). It
refers to a level of learning that each pupil attains when he / she is
able to give at least 80% correct responses on a unit test that has been
constructed based on instructional objectives with respect to that unit. Carroll (1963) explained the
concept of mastery theoretically which was transformed into a learning strategy
by Bloom (1968). Research efforts since then have been going on for establishing
the effectiveness of the strategy and also to modify the strategy for better
results.

Mastery Learning
Instructional Strategy (MLIS) is a plan, developed explicitly and
systematically to ensure that the learner achieves the expected instructional
objectives. It starts with concrete experiences involving actions on the part
of the learner and proceeds gradually to the abstract experiences. Such a
strategy is based on the theory of instruction as propounded by Bruner, for
teaching concepts in Mathematics. The advantage of presenting learning
experiences on a concrete to abstract continuum is that those learners who
possibly operate at the concrete level find the concrete representations of
abstract concepts in Mathematics more amenable for conceptualization. Further,
the instructional strategy provides optimum time for learning by employing a
mastery-learning paradigm, since the outcome expected is the mastery of the
competencies in Mathematics. The MLIS provides learning experiences which are
appropriate to the level at which a learner can process information. As a
result of this, the learners have a high rate of success experience. It is in
this background, a Mastery Learning Instructional Strategy based on the
“concrete to abstract” learning continuum for attainment of competencies in Mathematics
at the primary level was developed and its effectiveness was experimentally
tested.

**OBJECTIVES**

1. To develop a mastery
learning instructional strategy (MILS) based on concrete to abstract learning
continuum for the attainment of competencies in Mathematics;

2. To validate the
instructional strategy in terms of content accuracy and organization; and
language comprehensibility;

3. To study the
effectiveness of the instructional strategy in terms of mastery of competencies
in Mathematics; and learners’ liking towards mathematics.

**HYPOTHESES **

1. The mastery learning
instructional strategy (MLIS) is effective in enabling mastery of competencies
in Mathematics;

2. The MLIS is effective in
developing a liking towards study of Mathematics;

3. The MLIS and the
conventional approach have differential effect on mastery of competencies in
Mathematics;

4. The MLIS and the
conventional approach have differential effect on students’ liking towards
Mathematics.

**VARIABLES **

**Independent Variables**:

The instructional strategy
based on concrete-abstract learning continuum for teaching mathematics; the level of
mastery of pre-requisite competencies; and the home background of the
students.

**Dependent Variables: **

Achievement
of the minimum levels of learning in Mathematics and students’ liking towards
Mathematics.

**METHOD **

**Sample**

The sample of the study consisted of a total
of 129 students of standard II from two schools: one experimental and one* *conventional. The two groups were matched on the basis of
pre-requisite competencies in mathematics comprising of first standard
competencies, sex, age, parental education, availability of academic help at
home and students liking towards mathematics using c^{2} test.

**Tools **

A criterion referenced
achievement test was developed to measure the pre-requisite competencies of the
students in Mathematics. The learners’ liking towards Mathematics was measured
on an interview schedule developed for the purpose.

**Procedure**

The pre-test-post-test
matched group design was employed in this study. MLIS based on concrete to
abstract learning continuum for the attainment of competencies in Mathematics
of standard II was developed. It was designed as per the formulations of
Benjamin Bloom for a group-based and teacher-paced strategy. The broad areas of
second standard Mathematics identified for developing the MLIS were
‘Understanding the whole numbers and numerals’, and ‘Understanding geometrical
shapes’. There were a total of 15 competencies under these two areas. The MLIS consisted of
concrete, semi-abstract and abstract level activities and games for each
competency with formative tests and enrichment activities for ‘masters’ in the
first formative test. The MLIS developed was validated in terms of content
accuracy and organisation, and language comprehendability.** **Implementation
of MLIS in classroom involved four major steps viz.,** **defining for
mastery, planning for mastery, teaching for mastery, and grading for mastery.*
*The implementation took in to account the components of MLIS viz.,
‘Orienting students for mastery’, ‘Specification of instructional objectives’, and
‘Determination of mastery standard’. MLIS was implemented at concrete,
semi-abstract and abstract level for all competencies. First formative test was
administered after the implementation of MLIS for each competency or for
similar competencies. The formative tests developed in the MLIS were also
criterion referenced achievement tests and scoring was done following the same
procedure as used for scoring the criterion referenced achievement test scores
to measure the pre-requisite competencies of the students. Based on the
formative test performance, number of masters and non-masters were identified.
Non-masters were provided remedial instruction and activities and second
formative test was administered. Number of masters and non-masters were
identified based on their performance on the second formative test. Non-masters
were provided remedial instruction till they mastered the competency.The
summative test to measure the competencies considered in the MLIS was
administered after implementation of the strategy. Data obtained were analysed using c^{2} test and
z-test for their significance.

**ANALYSIS AND
INTERPRETATION **

Effectiveness of the MLIS
was determined in terms of achievement of competencies in mathematics and
learners liking towards mathematics. In the** **Experimental School, the
effectiveness of the strategy was established by finding the number of masters
of each of the fifteen competencies considered in the MLIS and number of
masters of overall competency (that is who have mastered 12 or more of the
individual competencies). Significance
of proportion of masters and significant proportion for each competency were
obtained for the first formative test, the second formative test and the
summative test. The
proportion of masters in all the competencies and overall
competency in the first formative test were more than the expected proportion
of 0.70 to be significant at 0.05 level. Obviously, the proportion of masters
in all the individual competencies and overall competency in the second
formative test and summative test was also more than the expected proportion of
0.70 to be significant at 0.05 level. Hence, MLIS was
successful in producing significant proportion of masters at 0.05 level on the first formative test itself in the experimental
group.

After arranging data on a four-point scale from mild and high
liking or disliking, the proportions of students with high and mild liking and
disliking on pre-test and post-test were calculated. There was a shift from
disliking to liking after the implementation of the MLIS. With a view to test
the significance of the shift, a ‘z-test’
was conducted. The two levels of liking and the two levels of disliking
were combined to produce a dichotomous data. The two categories were called
“liking” and “disliking” for Mathematics. The z-value (5.40) obtained was
significant at 0.01 level. This indicates that the shift observed from
disliking to liking towards Mathematics as a result of teaching through the
MLIS was significant. The effectiveness of the MLIS was measured by comparing
the achievement of competencies of the experimental group students with that of
the conventional group students. This was done by finding the significance of
difference between proportion of masters of individual and overall competencies
in mathematics of experimental group and the control group. It was found that all the
students in the experimental group had
mastered all the individual competencies. All of them were overall masters of
the competencies in Mathematics. In the control group, for four individual
competencies, the proportion of masters were more than the expected proportion
of 0.73 and hence, significant. For all the remaining eleven individual as well
as overall competencies, observed proportion of masters were less than the
expected proportion of masters and hence, not significant at 0.05 level. Hence, all students
learning through the MLIS had attained cent percent mastery of competencies,
whereas conventional approach had produced significant proportion of masters on
only four competencies. In experimental group, 98 per cent showed a liking towards Mathematics,
whereas in conventional group only 52 per cent
showed a liking towards Mathematics. The c^{2}-value
(49.77) obtained was significant.** **

The Mastery Learning
Instructional Strategy for teaching Mathematics at standard II was found to be
effective in producing significant proportion of masters. There was a
significant gain in the students’ liking for mathematics as a result of
learning through the mastery learning instructional strategy. A significant
difference was found in achievement of competencies in Mathematics between the
students taught by the investigator using the MLIS and those taught by the
teacher using conventional approach. Significant difference was found between
the experimental group students and comparison group students in their liking
for Mathematics.

**CONCLUSION**

All the pupils taught
through the MLIS mastered all competencies in mathematics. Pupils taught
through MLIS develop high liking towards Mathematics as it provides opportunities to play and
perform activities as well as the success experiences that they get while
learning.

**REFERENCES**

Block, J.
(1971) *Mastery Learning: Theory and Practice*. Holt, Rinehart, &

Bloom, B. (1968) Learning
for mastery.* Evaluation Comment* 1, 2, 1-5.

Bloom, B. (1971) *Mastery
Learning*. Holt, Rinehart, &

Bruner, J.S.(1966) *Towards a Theory of Instruction*.

Carroll, J. (1963*) *A model for school
learning. *Teachers College Record* 64, 723-733.

Guskey, T. & Gates, S. (1986) Synthesis of research on
the effects of Mastery Learning in elementary and secondary classrooms. *Educational
Leadership* 43, 8, 73-80.

Patterson, W. (1993)* *Moving
toward mastery learning*: *one school’s approach*.* *NASSP Bulletin* 77, 554, 96-99.